On Scalable and Efficient Computation of Large Scale Optimal Transport

Abstract

Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework called SPOT (Scalable Push-forward of Optimal Transport). Specifically, we approximate the optimal transport plan by a pushforward of a reference distribution, and cast the optimal transport problem into a minimax problem. We then can solve OT problems efficiently using primal dual stochastic gradient-type algorithms. We also show that we can recover the density of the optimal transport plan using neural ordinary differential equations. Numerical experiments on both synthetic and real datasets illustrate that SPOT is robust and has favorable convergence behavior. SPOT also allows us to efficiently sample from the optimal transport plan, which benefits downstream applications such as domain adaptation.

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Cited by in corpus (3)

• Optimal transport mapping via input convex neural networks
• Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks
• Large-Scale Optimal Transport via Adversarial Training with Cycle-Consistency